I have been going over the tutorials and I understand pretty much everything in there but in the 2 complex logic ones i dont understand how they got the beginning of the puzzle. Im confused by the very first picture and I am thinking I miss something basic. Any help would be greatly appreciated!!

- First, look at the 8th collumn (the one with the 4,1,1....1,2 clues). If you start filling it from the bottom (2, then 1, etc...), so that the clues are placed as close to each other as possible, the 4-clue will end in the square that's marked on the 4th row. If, on the other hand, you start filling from the top, the 4-clue will of course also end with this square. So, no matter how the clues are placed, this square is part of the 4-clue, and this is black.

- Now, the 6-3-1 line - again, no matter if you put the clues as left as you can or as right as you can, the 3 marked squares will be part of the 6-clue, so we can mark them black.

- The same process gives us the square in the third collumn from the left (1-2-3-6), which must be part of the 6-clue. When you look at the row for this square (5-2), you can see that the square has to be part of the 2 (it can't be part of the 5, because then you don't have enough space for a blank square and a 2-black sequence). That means the right-most square in this row can't be black (if it is, it's a sequence longer than 2...)

I hope that helped! If it wasn't clear enough, just say so, and I can attach detailed pictures to explain what I mean.